Inverse problems for one-dimensional fluid-solid interaction models

We consider a one-dimensional fluid-solid interaction model governed by the Burgers equation with a time varying interface. We discuss on the inverse problem of determining the shape of the interface from Dirichlet and Neumann data at one end point of the spatial interval. In particular, we establis...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2024-01
Main Authors: Apraiz, J, Doubova, A, Fernández-Cara, E, Yamamoto, M
Format: Article
Language:English
Subjects:
Burgers equation
Dirichlet problem
Estimates
Fluid-solid interactions
Interaction models
Interpolation
Inverse problems
Lateral stability
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider a one-dimensional fluid-solid interaction model governed by the Burgers equation with a time varying interface. We discuss on the inverse problem of determining the shape of the interface from Dirichlet and Neumann data at one end point of the spatial interval. In particular, we establish uniqueness results and some conditional stability estimates. For the proofs, we use and adapt some lateral estimates that, in turn, rely on appropriate Carleman and interpolation inequalities.
ISSN:2331-8422